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This article is cited in 1 scientific paper (total in 1 paper)
Path Integrals on Euclidean Space Forms
Guillermo Capobianco, Walter Reartes Departamento de Matemática, Universidad Nacional del Sur,
Av. Alem 1253, 8000 Bahía Blanca, Buenos Aires, Argentina
Abstract:
In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, based on the reproducing property of this space, is proposed. In the $\mathbb{R}^n$ case the obtained results coincide with the known expressions.
Keywords:
path integrals; holomorphic quantization; space forms; reproducing kernel Hilbert spaces.
Received: July 9, 2015; in final form August 31, 2015; Published online September 3, 2015
Citation:
Guillermo Capobianco, Walter Reartes, “Path Integrals on Euclidean Space Forms”, SIGMA, 11 (2015), 071, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1052 https://www.mathnet.ru/eng/sigma/v11/p71
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Abstract page: | 134 | Full-text PDF : | 30 | References: | 32 |
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